Question

The gyro-magnetic ratio of an electron in an $H$-atom, according to Bohr model, is

• A. positive.
• B. increases with the quantum number $n$.
• C. negative.
• D. independent of which orbit it is in.

Answer 1

Answer: (C), (D)

independent of which orbit it is in.

As we know,

Angular momentum of electron $\left(L\right)$ is given by,

$L=\frac{nh}{2\pi }$ ..$\left(i\right)$

Magnetic moment of electron (𝑀) is given by,

$L=\frac{eh}{\left(4\pi m\right)}$ ..$\left(ii\right)$

Therefore, gyromagnetic ratio is given by,

$\text{Gyromagnetic ratio}=\frac{\text{magnetic moment}}{\text{angular momentum}}$

$=\frac{M}{L}$

By putting the values from equation $\left(i\right)$ & $\left(ii\right)$ we get,

$\text{Gyromagnetic ratio}=\frac{\frac{neh}{\left(4\pi m\right)}}{\frac{nh}{2\pi }}$

$=\frac{e}{2m}=constant$

As the value of $e$ is negative, so ratio will also be negative and as the equation shows it is independent of orbit.

$\text{Final Answer}:$ (a), (b)